Quick action from the driver of the bus saved the woman's life even though she suffered physical injuries.
He was taken to a south London police station for questioning.
In the video, the woman walks into the path of a male jogger who pushes her onto the ground.
A footage shows the man jogging approaching the woman and he seemingly appears to have pushed the woman onto the road.
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The incident happened at around 7am on Friday May 5 but an appeal to find the jogger was only launched this week.
An appeal was launched Monday for witnesses or anyone who recognizes the jogger in the footage.
Officials released surveillance footage of the incident Tuesday, and received "a good response" after asking the public for information, police said.
The Met said the man officers arrested was still the subject of investigation but had not been released on official police bail. The approaching bus had to swerve out the way, narrowly avoiding a collision. Police said he returned about 15 minutes later but ignored the victim's efforts to speak with him.
Passengers later got off the bus and came to the aid of the woman, who sustained minor injuries.